The Lunar Forge is situated at the top of the Silent Moons ruins, North-West of Whiterun:

During the day, this forge can be used to make any weapon you can make at any other ordinary forge:

At night, between 9 pm and 5 am, things are different. On the nearby workbench, you'll find a book that describes the effects the forge applies to weapons made, and used, during the night, "when the moons are out":

The Lunar Forge enchantment:

As described in the book, the Lunar Forge enchantment absorbs a (relatively) small amount of health from the target. This enchantment is levelled: 10, 20 or 30 points during 3 seconds per hit.

The enchantment being apparently given by the Moons themselves, it cannot be learnt.

For the same reason, the weapons never need to be refilled; their charge is constant.

Crafting the weapons:

The level of enchantment applied to the weapons depend on the player's level at smithing:

under 30, you'll make weapons that absorb 10 points of health from the target during 3 seconds,

between 30 and under 60, you'll make weapons that absorb 20 points of health from the target during 3 seconds,

from level 60, you'll make weapons that absorb 30 points of health from the target during 3 seconds.

Examples in images, using war hammers (the same apply to the other weapons, of course):

Improving the weapons:

The weapons made can be improved at any sharpening wheel, even if you don't have the Arcane perk. Examples in images, using war hammers (the same apply to the other weapons, of course):

Pros and cons of using these weapons:

It's up to you to decide which is a "pro" or a "con":

the weapons can be made at the Lunar Forge only, between 9 pm and 5 am, any day,

the enchantment apply to iron and steel weapons, one handed and two handed; bows excepted,

the enchantment cannot be learned at an enchanting table and applied to other weapons (the reason is that this enchantment is added by the moons and exists outside the scope of scholarly knowledge),

the enchantments are constant: no need to use soul gems to recharge the weapons,

the enchantment works at night between 9 pm and 5 am.

The weapons created are lighter and faster than their counterparts. Comparison:

Iron weapons:

Iron Battleaxe: weight 20, speed 0.7,

Lunar Forge Iron Battleaxe: weight 18, speed 0.8,

Iron Dagger: weight 2, speed 1.3,

Lunar Forge Iron Dagger; weight 1.5, speed 1.4,

Iron Great Sword: weight 16, speed 0.7,

Lunar Forge Iron Great Sword: weight 14, speed 0.9,

Iron Mace: weight 13, speed 0.8,

Lunar Forge Iron Mace: weight 12, speed 0.9,

Iron Sword: weight 9, speed 1.0,

Lunar Forge Iron Sword: weight 8, speed 1.1,

Iron War Axe: weight 11, speed 0.9,

Lunar Forge Iron War Axe: weight 10, speed 1.0,

Iron War Hammer: weight 24, speed 0.6,

Lunar Forge Iron War Hammer: weight 22, speed 0.7.

Steel weapons:

Steel Battleaxe: weight 21, speed 0.7,

Lunar Forge Steel Battleaxe: weight 19, speed 0.9,

Steel Dagger: weight 2.5, speed 1.3,

Lunar Forge Steel Dagger; weight 2.0, speed 1.3, (speed unchanged)

Steel Great Sword: weight 17, speed 0.7,

Lunar Forge Steel Great Sword: weight 15, speed 0.9,

Steel Mace: weight 14, speed 0.8,

Lunar Forge Steel Mace: weight 13, speed 0.9,

Steel Sword: weight 10, speed 1.0,

Lunar Forge Steel Sword: weight 9, speed 1.1,

Steel War Axe: weight 12, speed 0.9,

Lunar Forge Steel War Axe: weight 11, speed 0.9, (speed unchanged)

Steel War Hammer: weight 25, speed 0.6,

Lunar Forge Steel War Hammer: weight 23, speed 0.7.

Side notes:

I added a tanning rack near the forge; it had always bugged me that there was no tanning rack there.

The vanilla broken Lunar Forge weapons that were laying around near the forge and inside the ruins have been disabled and replaced by new ones.

Incompatibilities:

Any other mod that handles the Lunar Forge weapons or modifies the place.

Installation:

if you are using this mod with Skyrim Special Edition, download the "LunarForgeWeaponsSE.zip",

if you are using this mod with Skyrim, download the "ladyonthemoonsLunarForgeWeapons.zip",

and extract the content of the archive into C:\Program Files\Steam\steamapps\common\Skyrim\Data. Launch the game and make sure the esp is selected in the launcher "Data Files".